Theoretical study of the dependences of the young’s and torsion moduli of thin single-layer carbon zigzag and armchair nanotubes on the geometric parameters

The Young’s and torsion moduli of single-layer carbon (m, 0) and (m, m) nanotubes are studied. It is demonstrated that both moduli depend on the chirality, diameter, and length of the nanotube. It is found for the first time that the torsion modulus increases with the nanotube diameter and diminishes with an increase in its length. By considering nanotubes with various values of the diameter-to-length ratio, it is shown that the Young’s and torsion moduli of the nanotubes saturate at a diameter-to-length ratio of ～0.3. The values of the torsion modulus as calculated from the Young’s modulus we obtained and from the deformation energy do not coincide, which can be attributed to the effect of dangling bonds at the open ends of the nanotubes. Energy calculations are performed using the Goodwin modification of the semiempirical Harrison tight-binding method.     

Experiment investigation on effects of elastic modulus on cavitation erosion of silicone rubber

Research into cavitation phenomena in various fields shows that the elastic modulus of a boundary has a potential impact on cavitation erosion. To obtain the direct relationship between the elastic modulus of the boundary and cavitiation erosion, single-layer samples with different chemical composition and moduli, and double-layer samples with different elastic moduli and the same surface layer material, were prepared with silicone rubber. The results of cavitation experiments on single-layer samples, show that the coating chemical composition and mechanical properties together affect the cavitation morphology of the coating, and dominant factors vary with erosion stage. Through the cavitation test of double-layer samples, it was found that there is a positive correlation between the elastic modulus of the coating and the degree of cavitation. This study helps us to understand the relationship between coating elastic modulus and cavitation more directly, and provides theoretical and technical guidance for the application of anti-cavitation for elastic coating in engineering.     

Temperature effect on the elastic properties of yttrium garnet ferrite Y<Subscript>3</Subscript>Fe<Subscript>5</Subscript>O<Subscript>12</Subscript>

The Young’s moduli along the [100] and [110] crystallographic directions and the shear modulus along the [100] direction in a high-purity yttrium garnet ferrite single crystal are measured in the temperature range from 20 to 600°C. All the independent elastic constants are calculated for this temperature range. The behavior of the elastic moduli and elastic anisotropy factor is analyzed in the vicinity of the critical temperature of the magnetic phase transition.     

Specific features of the determination of the mechanical characteristics of thin films by the nanoindentation technique

The hardness and the elastic modulus of Cu thin films on Si, Ti, Cu, and Al substrates are investigated. It is demonstrated that the use of the Oliver-Pharr method in combination with the technique for evaluating the true hardness makes it possible to determine uniquely the hardness of Cu thin films at different ratios between the hardnesses of the film and the substrate. The elastic modulus of thin films can be correctly measured by the Oliver-Pharr method only in the case where the film and the substrate exhibit identical elastic properties. In order to determine the elastic moduli of films with the use of the parameter P/S ², the film and the substrate should have close values of both the hardness and the elastic modulus.     

Boron–Carbon Nanocomposites Fabricated at High Pressures and Temperatures

Interaction of amorphous boron and C₆₀ fullerite is analyzed at pressures of 2.0 and 7.7. GPa and temperatures of 600–1800°C. Effect of pressure and temperature on the material structure is studied, temperatures for synthesis of boron carbide and diamond are found, and the sequence of transformations of the carbon component is determined. Ultrasonic method is used to measure elastic moduli of the samples, and the dependences of the moduli on the structure are analyzed. It is demonstrated that the boron–carbon nanocomposite synthesized at relatively low pressure (2.0 GPa) and temperature (about 1000°C) exhibits high elastic parameters (bulk modulus, B ≈ 75.3–84.0 GPa; Young modulus, E ≈ 108–119 GPa; and shear modulus, G ≈ 43–47 GPa at a density of about 2.2 g/cm³). The results can be used for development of novel nanocomposite materials.     

Nondestructive evaluation of high‐temperature elastic modulus of 3C‐SiC using Raman scattering

A nondestructive method is reported to measure the high‐temperature modulus of 3C‐SiC coating and bulk samples using Raman scattering. Within the temperature range from 20 °C to 900 °C, both the longitudinal optical and transverse optical phonon frequencies decrease linearly as the temperature increases. The elastic moduli derived from the longitudinal optical phonon agree with previous results measured using other techniques. It is further shown that the grain size and impurity only have a negligible effect on the elastic modulus of 3C‐SiC. Copyright © 2011 John Wiley & Sons, Ltd.     

Time-Dependent Resonant Tunneling in a Double-Barrier Diode Structure

The elastic moduli of bilayer graphene nanomeshes, i.e., nanomeshes of bilayer graphene, where layers at the edges of “closed” holes are coupled to each other by a continuous network of sp²-hybridized atoms, have been calculated by ab initio methods. Structures with different configurations of holes in layers with AA, AB, and 30° stackings have been studied. It has been shown that the ultimate tensile strength of the nanomeshes under consideration is higher than that of graphene nanostructures and is comparable with the ultimate tensile strength of bilayer graphene and single-layer carbon nanotubes. A possible application of such strong nanomeshes as nanocontainers for hydrogen storage and other compressed gases has been also discussed.

     

Molecular forces and elastic constants of polyethylene single crystals

Polyethylene has an orthorhombic lattice for which nine elastic constants exist; they are obtained in terms of the intra- and intermolecular forces. Constants involved in the 6-12 Lennard-Jones potential approximating the London dispersion type of van der Waals' forces are obtained by computing the crystal potential energy and comparing it with the cohesive energy. First and second nearest-neighbor interactions are considered to establish relationship between the elastic constants and the interaction constants. The latter are obtained in terms of the C—C bond, stretching, bending, and repulsive force constants and the L-J potential constants. A limited type of central force assumption is applied. Values of Young and shear moduli are obtained along the three axes. The value along the chain compares with the experimentally determined and calculated values for oriented polyethylene. Young's modulus along the lateral direction is of the order of Young's modulus of bulk polyethylene, showing that intermo-lecular forces are the ones that determine the Young modulus of bulk polyethylene.     

The effect of heat setting on the elastic and viscoelastic properties of nylon-6 films

The elastic and viscoelastic properties of nylon-6 films with different structural forms and different degrees of crystallinity, obtained by heat setting nylon-6 films at various temperatures, without constraint, have been investigated. The elastic modulus increases with increasing degree of crystallinity. The values of the transverse elastic moduli for completely amorphous and completely crystalline samples have been calculated on the basis of these results. The measurements of dynamic mechanical properties were carried out at two different frequencies, viz., 11 Hz and 110 Hz, over a range of temperature from room temperature to 150°C under ambient conditions of humidity. It is observed that the moisture content increases whereas the glass transition temperature decreases with increasing temperature of pretreatment. The activation energy of the α transition has also been calculated.     

Temperature Effect on the Elasticity of Acrylamide-n-Isopropylacrylamide Copolymers

Acrylamide (AAm) – N-isopropylacrylamide (NIPA) copolymers were prepared via free radical crosslinking copolymerization with various weight percentages (wt%) of AAm and NIPA. The temperature dependence of the compressive elastic modulus, G, and toughness, U_T, of the PAAm- NIPA copolymers due to a volume phase transition was found using a compressive testing technique. It was observed that the compressive elastic modulus increased comprehensively when the temperature was increased between 30°C and 60°C. The PAAm- NIPA copolymers presented higher values of the compressive elastic modulus than pure NIPA above the lower critical solution temperature (LCST) (NIPA exhibits a volume phase transition from hydrophilic to hydrophobic in water at 31°C) and their compressive elastic modulus and toughness had a strong temperature dependence.     

Effect of heat treatment on the mechanical and microstructural characterization of Mg-AZ91E/TiC composites

Mg-AZ91E/TiC_p composite was fabricated using a spontaneous infiltration technique at 950 °C under an argon atmosphere. The composites produced have 37 vol.% of metal matrix and 63 vol.% of TiC-like reinforcement. The obtained composites were subsequently solution heat-treated at 413 °C during 24 h, cold water quenched, and subsequently artificially aged at 168 and 216 °C during 16 h in an argon atmosphere. Effect of heat treatment on the microstructure and mechanical properties was evaluated. Microstructural characterization was analyzed using different techniques such as X-ray diffraction (XRD) and scanning electron microscopy (SEM). Interface between matrix and reinforcement was examined using transmission electron microscopy (TEM), and mechanical properties were evaluated by measuring the elastic modulus and hardness. Mg, TiC, Al, and Mg₁₇Al₁₂ phases through XRD were detected. Meanwhile, using TEM analysis in heat-treated composites MgAl₂O₄, MgO, and Al₂O₃ were identified. The as-fabricated composite have elastic modulus and hardness of 162 GPa and 316 Hv, respectively. After solution heat treatment and aging at 168 °C during 12 h, the composites reaches values of 178 GPa and 362 Hv for the elastic modulus and hardness, respectively. Time of aging was correlated with measures of elastic modulus and hardness.     

Effect of native oxides on the elasticity of a silicon nano-scale beam

Native oxide is usually formed during the fabrication of silicon beams. A model is developed to describe the effect of native oxide on the elastic modulus of the silicon nano-beam based on the semi-continuum method. The model predicts that Young’s modulus of the nano-beam with native oxide increases as the nano-beam thickness decreases while it exhibits opposite behavior without native oxide. Native oxide dominates the beam with its scaling down to several nanometers. Young’s moduli are in the range from 123 GPa to 190 GPa when the thickness is several nanometers, and they approach the bulk value when the thickness is greater than about 500nm.     

空位结构缺陷对C纳米管弹性性质的影响

用分子动力学方法对不同空位缺陷的扶手椅型与锯齿型单壁C纳米管杨氏弹性模量进行了计算和分析. 结果表明：扶手椅型（5, 5）, （10,10）和锯齿型（9, 0）, （18, 0） 纳米管在无缺陷时其杨氏模量分别为948,901和804,860 GPa. 随管径的增大,扶手椅型和锯齿型单壁C纳米管弹性模量分别减小和增大,表现出完全不同的变化规律. 随着C纳米管中单点空位缺陷的均匀增加,杨氏模量下降,当缺陷比率增加到一定程度时,杨氏模量下降骤然趋缓,形成一下降平台;双空位缺陷对C纳米管杨氏模量的影响与其分布方向有关;随单点空位缺陷间原子数的增加,在轴向上,杨氏模量下降到某一值小幅波动,而在周向上杨氏模量先下降,然后上升到某一稳定值. 随两单点空位缺陷的空间距离进一步增大,杨氏模量又呈微降趋势. 通过分子间σ键与π键特征及缺陷间近程电子云耦合作用规律与空位缺陷内部5-1DB缺陷的形成特点等理论对上述规律进行了分析. 关键词： 空位缺陷 C纳米管 分子动力学 杨氏模量     

Multiscale modeling of graphene- and nanotube-based reinforced polymer nanocomposites

A combination of molecular dynamics, molecular structural mechanics, and finite element method is employed to compute the elastic constants of a polymeric nanocomposite embedded with graphene sheets, and carbon nanotubes. The model is first applied to study the effect of inclusion of graphene sheets on the Young modulus of the composite. To explore the significance of the nanofiller geometry, the elastic constants of nanotube-based and graphene-based polymer composites are computed under identical conditions. The reinforcement role of these nanofillers is also investigated in transverse directions. Moreover, the dependence of the nanocomposite?s axial Young modulus on the presence of ripples on the surface of the embedded graphene sheets, due to thermal fluctuations, is examined via MD simulations. Finally, we have also studied the effect of sliding motion of graphene layers on the elastic constants of the nanocomposite.     

Elasticity of BaFCl single crystal under hydrostatic pressure

The sound velocities for longitudinal and transverse waves have been measured in single crystalline BaFCl at room temperature using ultrasonic pulse echo and Brillouin scattering techniques. The complete set of elastic constants is deduced and lead to the bulk moduli values of BaFCl at ambiant conditions (, , ) which are compared with those obtained by a shell model. Moreover, using the ultrasonic technique under pressure, the pressure derivatives of the second order elastic constants at 298 K have been determined up to 0.3 GPa. All moduli increase linearly with pressure in this pressure range, allowing to determine directly and separately the first derivative of the bulk modulus B'₀ = 5.8. These data are used to calculate a Murnaghan equation of state. A detailed comparison is given between our results with those recently obtained by X-ray diffraction on powder or calculated using the local density approximation method. Finally, the anisotropy of BaFCl under pressure is discussed. Received: 19 March 1998 / Revised: 15 May 1998 / Accepted: 19 May 1998     

Electronic properties of pan-based carbon fibers—I: Experiment and comparison with properties of bulk carbons

Measurements of the resistivity of PAN-based fibers are reported for temperatures between 1.5 and 300 K. Particular care was taken to avoid sample heating problems during measurements. Fibers were heat-treated between ~ 1300°C to above 3000°C, corresponding to a wide range of elastic moduli (~ 35–112 Msi : 240–770 GPa). A particularly surprising result was the observation of a resistivity maximum for low modulus (35 Msi ~240 GPa) fiber below 50 K. Results are compared to those reported on bulk heat treated carbons and pyrocarbons. A qualitative discussion of the results is also given in terms of recent models of the electronic energy levels of carbon ribbons and turbostratic carbons.     

Ab initio investigation of the pressure influence on elastic properties of the GaS layered compound

From first principles, in the pressure range of 0–20 GPa, taking into account the structural phase transition at 3 GPa, all independent elastic constants of GaS compound have been calculated. From obtained data, the pressure dependences of the velocities of propagation of elastic waves in different symmetry directions have been determined. The values of averaged elastic moduli, Young’s modulus and Poisson’s ratio and their pressure dependence have also been calculated..     

Imaging the elastic properties of coiled carbon nanotubes with atomic force microscopy

Coiled carbon nanotubes were produced catalytically by thermal decomposition of hydrocarbon gas. After deposition on a silicon substrate, the three-dimensional structure of the helix-shaped multiwalled nanotubes can be visualized with atomic force microscopy. Helical structures of both chiralities are present in the nanotube deposits. For larger coil diameters ( >170 nm), force modulation microscopy allows one to probe the local elasticity along the length of the coil. Our results agree with the classical theory of elasticity. Similar to the case of straight nanotubes, the Young modulus of coiled multiwalled nanotubes remains comparable to the very high Young modulus of hexagonal graphene sheets.     

Analysis of Single-Walled Carbon Nanotubes Using a Chemical Bond Element Model

提出了一种纳米尺度的有限元方法,碳纳米管中的碳-碳化学键被模拟为键单元．按照平衡关系,根据有限元理论,作用于每个碳原子上的作用力可以写成键单元的刚度矩阵与每个碳原子位移的乘积．在分子力学的基本假设下,键单元刚度矩阵的每个元素可以写为分子力学中力场常数的函数,这样建立起了宏观力学方法(有限元)与纳米尺度力学方法(分子力学)之间的联系．应用该方法模拟了扶椅型与锯齿型单壁碳纳米管的力学行为从而验证了该方法的有效性．分析结果说明单壁碳纳米管的弹性模量与管厚度的选取直接相关．此外,弹性模量对所选取的分子力学中的力场常数非常敏感,管的弹性模量显示出对半径的尺度依赖性,但是管长度对弹性模量的影响小到可以被忽略．     

On mechanical characteristics of nanocrystals

The dependence of the elastic moduli of a nanocrystal on its size is investigated theoretically with reference to a two-dimensional single-crystal strip. It is shown that the uncertainty (of a fundamental nature) in the size of a nanocrystal causes the determination of many of its mechanical characteristics to be ambiguous. It is found that the Cauchy-Green relations are modified and the elastic-constant tensor ceases to be symmetric; the size and shape of a nanocrystal render its mechanical properties more anisotropic. For a single-crystal strip, the Poisson ratio decreases and the Young modulus increases with decreasing thickness of the strip; in the case of a very thin crystal film (two atomic layers thick), these elastic moduli can differ from their macroscopic values by a factor of two. The size effects which make the continuum elasticity theory inapplicable to nanocrystals are estimated. The size effects that occur when the molecular dynamics method is applied for modeling macroscopic objects are also discussed.